In the majority of known knitting machines of this type, the yarn changing devices are provided with a particular number of, for instance four, yarn fingers, such that in each knitting system comprising a knitting point and a yarn changing device, optionally either one of four yarns may be laid into the knitting tools (e.g. DE 27 10 045 A1, DE 28 05 779 A1, DE 31 29 724 C2, DE 195 11 949 A1). From time to time, however, there is a trend towards fabrics with stripe patterns (sometimes also called hooped patterns), which may be made from more than the given number, i.e. for instance, from five or more yarns per system. It has therefore already been proposed that yarn changing devices should be provided with five or more selectable yarn fingers. A problem resulting therefrom, however, is that the yarn fingers and the associated parts have to be made substantially thinner than previously if the yarn changing devices are to have the same overall width as with just four yarn fingers. A consequence of this is increased wear and lower operational reliability. If, however, the yarn fingers and the associated parts are made with the usual width, the result is a correspondingly increased width of the knitting systems overall. This is undesirable since the number of knitting systems that may be accommodated on the periphery of a circular knitting machine is thereby reduced. This, in turn, requires not only a new design of the knitting machine compared with a knitting machine whose yarn changing devices are equipped for only four yarns, but leads also to a knitting machine of reduced performance. The latter is particularly undesirable if the striping function is not needed at times or to the full extent which, due to the constantly changing dictates of fashion, could well be required.